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MULTIVARIATE MODELLING OF HOUSEHOLD CLAIM FREQUENCIES IN MOTOR THIRD-PARTY LIABILITY INSURANCE

Published online by Cambridge University Press:  08 June 2018

Florian Pechon ,
Julien Trufin  and
Michel Denuit
Florian Pechon*
Affiliation:
Institute of Statistics, Biostatistics and Actuarial Science, Université catholique de Louvain (UCL), Louvain-la-Neuve, Belgium
Julien Trufin
Affiliation:
Department of Mathematics, Université Libre de Bruxelles (ULB), Bruxelles, Belgium, E-Mail: [email protected]
Michel Denuit
Affiliation:
Institute of Statistics, Biostatistics and Actuarial Science, Université catholique de Louvain (UCL), Louvain-la-Neuve, Belgium, E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

Actuarial risk classification studies are typically confined to univariate, policy-based analyses: Individual claim frequencies are modelled for a single product, without accounting for the interactions between the different coverages bought by the members of the same household. Now that large amounts of data are available and that the customer's value is at the heart of insurers' strategies, it becomes essential to develop multivariate risk models combining all the products subscribed by the members of the household in order to capture the correlation effects. This paper aims to supplement the standard actuarial policy-based approach with a household-based approach. This makes the actuarial model more complex but also increases the volume of available information which eases and refines forecasting. Possible cross-selling opportunities can also be identified.

Keywords

Multivariate Poisson mixture modelPoisson-LogNormalPoisson–Gammanegative binomiala posteriori risk revaluation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 3 , September 2018 , pp. 969 - 993
Copyright
Copyright © Astin Bulletin 2018 

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References

Antonio, K., Guillen, M. and Perez Martin, A.M. (2011) Multidimensional credibility: A Bayesian analysis of policyholders holding multiple policies. Working Paper ASE-RI. Available at https://dare.uva.nl/search?identifier=1587a3ef-f8ec-41a7-b61a-ba44d8bfc5ae.Google Scholar
Barseghyan, L., Molinari, F., Morris, D.S. and Teitelbaum, J.C. (2016) Unobserved heterogeneity, experience rating, and insurance demand. Georgetown Law Faculty Publications and Other Works 1127. Available at https://scholarship.law.georgetown.edu/facpub/1127/.Google Scholar
Bühlmann, H. and Gisler, A. (2005) A Course in Credibility Theory and its Applications. Berlin: Springer.Google Scholar
Denuit, M., Dhaene, J., Goovaerts, M.J. and Kaas, R. (2005) Actuarial Theory for Dependent Risks: Measures, Orders and Models. New York: Wiley.Google Scholar
Denuit, M. and Lang, S. (2004) Non-life rate-making with Bayesian GAMs. Insurance: Mathematics and Economics, 35 (3), 627–647.Google Scholar
Denuit, M., Marechal, X., Pitrebois, S. and Walhin, J.-F. (2007) Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus–Malus Systems. New York: Wiley.Google Scholar
Englund, M., Guillen, M., Gustafsson, J., Nielsen, L.H. and Nielsen, J.P. (2008) Multivariate latent risk: A credibility approach. ASTIN Bulletin, 38, 137–146.Google Scholar
Englund, M., Gustafsson, J., Nielsen, L.H. and Nielsen, J.P. (2009) Multidimensional credibility with time effects: An application to commercial business lines. Journal of Risk and Insurance, 76, 443–453.Google Scholar
Fardilha, T., de Lourdes Centeno, M. and Esteves, R. (2016) Tariff systems for fleets of vehicles: A study on the portfolio of Fidelidade. European Actuarial Journal, 6, 331–349.Google Scholar
Frees, E.W.J., Meyers, G. and Cummings, A.D. (2010) Dependent multi-peril ratemaking models. ASTIN Bulletin, 40, 699–726.Google Scholar
Kroeze, K. (2016) MultiGHQuad: Multidimensional Gauss–Hermite quadrature. Available at: http://CRAN.R-project.org/package=MultiGHQuadGoogle Scholar
Narasimhan, B. (2016) Cubature: Adaptive multivariate integration over hypercubes. Available at: http://cran.r-project.org/package=cubatureGoogle Scholar
Shi, P. (2016) Insurance ratemaking using a copula-based multivariate Tweedie model. Scandinavian Actuarial Journal, 2016, 198–215.Google Scholar
Shi, P., Feng, X. and Boucher, J.P. (2016) Multilevel modeling of insurance claims using copulas. Annals of Applied Statistics, 10, 834–863.Google Scholar
Shi, P. and Valdez, E.A. (2014) Multivariate negative binomial models for insurance claim counts. Insurance: Mathematics and Economics, 55, 18–29.Google Scholar
Thuring, F., Nielsen, J.P., Guillen, M. and Bolance, C. (2012) Selecting prospects for cross-selling financial products using multivariate credibility. Expert Systems with Applications, 39, 8809–8816.Google Scholar
Weiser, C. (2016) mvQuad: Methods for multivariate quadrature. Available at: http://CRAN.R-project.org/package=mvQuadGoogle Scholar